Nonnegative matrix factorization with local similarity learning

High-dimensional data are ubiquitous in the learning community and it has become increasingly challenging to learn from such data [1]. For example, as one of the most important tasks in multimedia and data mining, information retrieval has drawn considerable attentions in recent years [2-4], where there is often a need to handle high-dimensional data. Often times, it is desirable and demanding to seek a data representation to reveal latent data structures of high-dimensional data, which is usually helpful for further data processing. It is thus a critical problem to find a suitable representation of the data in many learning tasks, such as image clustering and classification [5,1], foreground-background separation in surveillance video [6,7], matrix completion [8], community detection [9], link prediction [10], etc. To this end, a number of methods have been developed to seek proper representations of data, among which matrix factorization technique has been widely used to handle high-dimensional data. Matrix factorization seeks two or more low-dimensional matrices to approximate the original data such that the high-dimensional data can be represented with reduced dimensions [11,12]. For some types of data, such as images and documents, the entries are naturally nonnegative. For such data, nonnegative Existing nonnegative matrix factorization methods usually focus on learning global struc-ture of the data to construct basis and coefficient matrices, which ignores the local struc-ture that commonly exists among data. To overcome this drawback, in this paper, we propose a new type of nonnegative matrix factorization method, which learns local simi-larity and clustering in a mutually enhanced way. The learned new representation is more representative in that it better reveals inherent geometric property of the data. Moreover, the new representation is performed in the kernel space, which enhances the capability of the proposed model in discovering nonlinear structures of data. Multiplicative updating rules are developed with theoretical convergence guarantees. Extensive experimental results have confirmed the effectiveness of the proposed model. (c) 2021 Elsevier Inc. All rights reserved.